I watched this video on YouTube, which shows an Mi-26 taking off with its rotor tilted forward about 45 degrees. Is the video fake or is it real, and if it is real, how does the Mi-26 do such a thing?
It's real and it's simply the blades running at the flapping hinge limits with the cyclic stick full forward. The blade on the back is at its up limit and the one at the front at its down limit, resulting in an overall disc angle of about 30 degrees off horizontal. It's being done to accelerate along the ground as fast as possible. In the air, the machine's body will follow the tilt of the rotor quickly enough that this sort of angle is almost never experienced unless the pilot made a sudden extreme input in flight.
This (blades hitting flapping limits) is something that only multi-blade articulating rotors can tolerate. You can't do that with a two blade teetering rotor because contacting the blade flapping travel stops, known as mast bumping, will break the mast.